Question

已知(a+b)²=9,(a-b)²=4,求:(1)a×b的值;(2)a²+b²的值。

Answer 1

解：(1)∵(a+b)²=a²+2ab+b²,(a-b)²=a²-2ab+b²,
则a×b=[(a²+2ab+b²)-(a²-2ab+b²)]/4=(9-4)/4=5/4.
(2)由(1)可得，a²+b²=[(a²+2ab+b²)+(a²-2ab+b²)]/2=13/2.

Answer 2

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(a+b)²=9, ①
(a-b)²=4, ②
用①－②得，4ab=5
∴ab=5/4
用①＋②得，2(a²+b²)＝13
∴a²+b²＝13/2

Answer 3

(a+b)²-(a-b)²=9-5
(a+b+a-b)(a+b-a+b)=5
4ab=5
ab=5/4

(a+b)²+(a-b)²=9+5
a²+2ab+b²+a²-2ab+b²=14
2(a²+b²)=14
a²+b²=7

Answer 4

(a+b)²-(a-b)²=9-5
(a+b+a-b)(a+b-a+b)=5
4ab=5
ab=5/4

(a+b)²+(a-b)²=9+5
a²+2ab+b²+a²-2ab+b²=14
2(a²+b²)=14
a²+b²=7